Periodate oxidation of sugars
The vicinal-glycols can be cleaved to corresponding aldehydes and/or ketones in high yield by the action of periodic acid ($\ce{HIO4}$) or lead tetraacetate ($\ce{Pb(OAc)4}$). This oxidative cleavage of a carbon-carbon single bond provides a two-step involving cyclic intermediate reaction mechanism with high-yield. A generally accepted equation for these oxidations (A) is shown below:



The reaction using $\ce{HIO4}$ is called Malaprade Reaction (Ref.1), while that involving $\ce{Pb(OAc)4}$ is called Criegee Reaction. Malaprade Reaction is described as:


  The oxidation of adjacent diols with periodic acid or its salt in aqueous solution is generally known as the Malaprade reaction. Several solvents have been used to increase the solubility of organic substrates and the reaction proceeds faster under acidic conditions. This reaction has been further extended to the cleavage of $\alpha$‐hydroxy carbonyl compounds, 1,2‐dicarbonyl compounds, $\alpha$‐amino alcohols, $\alpha$‐amino acids, and polyhydroxy alcohols, and successfully applied for structural analysis.


Both cis- and trans-glycols (e.g., cis- and trans-cyclohexane-1,2-diols) undergo the oxidation with $\ce{HIO4}$ or its salts. As a rule, cis-glycols react more rapidly than trans-glycols and there is evidence for the presence of heterocyclic intermediates as shown in the diagram (B). For example, the publication by Buist, et al. (ref.2) revealed that cis-cyclohexane-1,2-diol cleaves about 20-times faster than trans-cyclohexane-1,2-diol. However, the equilibrium between the diol and the cyclic periodate intermediate (faster first step) slightly favors the trans-isomer (the ratio of cis/trans equilibrium constants is $400:1000$; Ref.2) while the rates of cleavage of cis-cyclohexane-1,2-diol to products is much faster compared to its trans-isomer (the ratio of cis/trans rate constants is $3300:165$; Ref.2). Thus, theoretically your believe of only cis-vicinal-diols would get oxidized with $\ce{HIO4}$ is completely wrong. 

Therefore, theoretically, each available $\ce{-C(OH)-C(OH) -}$ function would get oxidized ($\alpha$-methyl-D-glucopyranoside has 4 such functions), costing one $\ce{HIO4}$ molecule per function (Ref.3). However, rate of oxidation is depend on conditions, steric effects, $\mathrm{pH}$, etc. For example, the oxidation of $\alpha$-methyl-D-glucopyranoside by a solution of $\ce{HIO4}$ in pyridine has cleaved only the $\ce{C}$3$-\ce{C}$4 bond while the reaction of 6-O-trityl-$\alpha$-methyl-D-glucopyranoside is less selective under same condition and is directed to a greater degree to the $\ce{C}$2$-\ce{C}$3 bond (Ref.4).

References:


Zerong Wang, "Malaprade Reaction (Malaprade Oxidation)," In Comprehensive Organic Name Reactions and Reagents; John Wiley &amp; Sons, Inc.: New York, NY, 2010 (https://doi.org/10.1002/9780470638859.conrr406). ISBN: 9780471704508.
G. J. Buist, C. A. Bunton, J. H. Miles, “149. The mechanism of oxidation of α-glycols by periodic acid. Part V. Cyclohexane-1 : 2-diols,” J. Chem. Soc. 1959, 743-748 (https://doi.org/10.1039/JR9590000743).
Glen Dryhurst, In Periodate Oxidation of Diol and Other Functional Groups: Analytical and Structural Applications; First Edition, Pergamon Press: Oxford, United Kingdom, 1970. ISBN-10: 1483128385.
R. G. Krylova, S. N. Ryadovskaya, L. I. Kostelian, A. I. Usov, “Periodate oxidation of α-methyl-D-glucopyranoside, 6-O-trityl-α-methyl-D-glucopyranoside and 6-O-tritylcellulose in pyridine,” Bulletin of the Academy of Sciences of the USSR, Division of chemical science 1972, 21, 2005-2009 (https://doi.org/10.1007/BF00854627).